Related papers: A complete invariant for doodles on a 2-sphere
We study a global invariant for path structures. The invariant is obtained as a secondary invariant from a Cartan connection on a canonical bundle associated to a path structure. It is computed in examples which are defined in terms of…
We consider the degrees of the elements of a homogeneous system of parameters for the ring of invariants of a binary form, give a divisibility condition, and a complete classification for forms of degree at most 8.
This study defines finite-type invariants for curves on surfaces and reveals the construction of these finite-type invariants for stable homeomorphism classes of curves on compact oriented surfaces without boundaries. These invariants are a…
We describe the algebra of finite order invariants on the set of all $(n,2)$-torus knots.
We show how to define invariants of graphs related to quantum $\mathfrak{sl}(2)$ when the graph has more then one connected component and components are colored by blocks of representations with zero quantum dimensions.
We introduce new polynomial isotopy invariants for closed braids. They are constructed as polynomial valued {\em Gauss diagram 1-cocycles} evaluated on the full rotation of the closed braid $\hat \beta$ around the core of the corresponding…
For any chord diagram on a circle there exists a complete graph on sufficiently many vertices such that any generic immersion of it to the plane contains a plane closed curve whose chord diagram contains the given chord diagram as a…
In this paper we define novel topological invariants of doubly periodic tangles (DP tangles). DP tangles are embeddings of curves in the thickened plane with translational symmetries in two independent directions. We first organize the…
We define a new finite type invariant for stably homeomorphic class of curves on compact oriented surfaces without boundaries and extend to a regular homotopy invariant for spherical curves.
In this paper, we introduce a magneto-spectral invariant for finite graphs. This invariant vanishes on trees and is maximized by complete graphs. We compute this invariant for cycles, complete graphs, wheel graphs, hypercubes, complete…
We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.
This paper demonstrates an approach for developing a framework to produce invariants of base-point-free generic spherical curves under some chosen local moves from Reidemeister moves using based chord diagrams. Our invariants not only…
We take the fundamental group of the complement of the branch curve of a generic projection induced from canonical embedding of a surface. This group is stable on connected components of moduli spaces of surfaces. Since for many classes of…
Cubic complexes appear in the theory of finite type invariants so often that one can ascribe them to basic notions of the theory. In this paper we begin the exposition of finite type invariants from the `cubic' point of view. Finite type…
Using the definition of colouring of $2$-edge-coloured graphs derived from $2$-edge-coloured graph homomorphism, we extend the definition of chromatic polynomial to $2$-edge-coloured graphs. We find closed forms for the first three…
In this paper we define and investigate Z/2-homology cobordism invariants of Z/2-homology 3-spheres which turn out to be related to classical invariants of knots. As an application we show that many lens spaces have infinite order in the…
A hole is a chordless cycle with at least four vertices. A hole is odd if it has an odd number of vertices. A dart is a graph which vertices $a, b, c, d, e$ and edges $ab, bc, bd, be, cd, de$. Dart-free graphs have been actively studied in…
In this paper, we propose an approach to automatically compute invariant clusters for semialgebraic hybrid systems. An invariant cluster for an ordinary differential equation (ODE) is a multivariate polynomial invariant g(u,x)=0, parametric…
We give a complete invariant for shift equivalence for Boolean matrices (equivalently finite relations), in terms of the period, the induced partial order on recurrent components, and the cohomology class of the relation on those…
Chord diagrams and related enlacement graphs of alternating knots are enhanced to obtain complete invariant graphs including chirality detection. Moreover, the equivalence by common enlacement graph is specified and the neighborhood graph…